Question

Hi everyone! Here is a nasty rectangular to polar conversion, 4x^2-5y^2-36y-36=0...can anyone help solve for r? Thanks!

Answer 1

I have tried sooo many combinations and still can't get it

Answer 2

singing calc2 blues? lol

Answer 3

:o)

Answer 4

.......just plug in rsint and rcost......

Answer 5

i'm not creating parametric equations...just polar

Answer 6

by t I mean theta............

Answer 7

is your t meant to be a theta?

Answer 8

\[x= r \cos \theta\]
\[y= r \sin \theta\]

\[4x^2-5y^2-36y-36=0\]
\[4(r \cos \theta)^2-5(r \sin \theta)^2-36r \sin \theta-36=0\]
\[4r^2 \cos^2 \theta-5r^2 \sin^2 \theta-36r \sin \theta-36=0\]

\[(4 \cos^2 \theta -5 \sin^2 \theta) r^2 -(36 \sin \theta) r - 36 =0\]

from here i would assume is just a messy quadratic equation

Answer 9

i've to that point before...i just can't solve for r

Answer 10

same story...you can solve for r by using the quad formula

Answer 11

i can?

Answer 12

i mentioned messy right

\[r= \frac{-b \pm \sqrt{b^2- 4ac}}{2a}\]

Answer 13

yes

Answer 14

..............but it's gonna look ugly along the line........

Answer 15

unless you can find an nice transformation that i cant remember off the top of my head

good luck

Answer 16

the final answer is quite neat..........

Answer 17

there are like 4 solutions it could be, and none of them are ugly...

Answer 18

I said...ugly along the line

Answer 19

like -4/1+sin theta is an example...i just am having serious trouble getting towards that form

Answer 20

i will try the quadratic thingy...omg...this is gonna take awhile...can you periodically check in on me to see if i get it?

Answer 21

okay, I can see you're smart, so Imma help you out. \[\frac{ -6 }{ 3\sin(\theta) \pm 2}\]

Answer 22

woa...one of my choices as an answer is 6/2-3sin theta...that looks a little different than your plus or minus thingy...thingy is a technical term fyi :o)

Answer 23

ok...i'm gonna try and work this AGAIN...it might take awhile though...:o)

Answer 24

duhhh, that means there are two solutions, one with + and the other with -. lol

Answer 25

can i ask you a question?

Answer 26

if you bring the - from the 6 down, it swaps the position of the 2 and 3sint

Answer 27

ask...........

Answer 28

what tipped you off that you should be using the quadratic formula? Is it kinda just one of those things where you sit back and recognize the bigger picture?

Answer 29

yeah........kinda. Once I saw an r and an r^2.........that meant quad.

Answer 30

neat...okay...i'm gonna try and work this out...brb...well not right back lol

Answer 31

yo, I already gave you the answer....and you seen it already in the options. I'm leaving and won't be able to confirm whatever you do if it takes longer than 2 minutes.

Answer 32

no problem...thanks so much for your help Prime!

Answer 33

Thanks. Tag me whenever......

Answer 34

ok :o)